Decay estimates for evolution equations with classical and fractional time-derivatives
Analysis of PDEs
2018-07-27 v1
Abstract
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving both standard and Caputo time-derivative, complex valued magnetic operators, fractional porous media equations and nonlocal Kirchhoff operators. Both local and fractional space diffusion are taken into account, possibly in a nonlinear setting. The different quantitative behaviors, which distinguish polynomial decays from exponential ones, depend heavily on the structure of the time-derivative involved in the equation.
Cite
@article{arxiv.1807.10041,
title = {Decay estimates for evolution equations with classical and fractional time-derivatives},
author = {Elisa Affili and Enrico Valdinoci},
journal= {arXiv preprint arXiv:1807.10041},
year = {2018}
}